NEW YORK, Nov 17 (Reuters) - Wall Street was set to end the week on a muted note on Friday, with major indexes slipping modestly, as investors weighed the fate of the Republicans' tax cut plan.

Investors have been hopeful that a tax bill under debate in Congress will boost corporate earnings and further fuel the stock market's record-setting run.

Congressional Republicans took important steps on Thursday toward the biggest U.S. tax-code overhaul since the 1980s, with the House of Representatives approving a broad package of tax cuts. The debate shifts to the Senate, where a bill has already encountered resistance within the Republican ranks.

A Reuters poll showed that nearly two-thirds of more than 60 economists said they were not confident the Trump administration would get the legislation passed this year.

"Everybody is looking at that tax plan and wondering exactly what are the devils in the details," said Bruce McCain, chief investment strategist at Key Private Bank in Cleveland.

The Dow Jones Industrial Average fell 96 points, or 0.41 percent, to 23,362.36, the S&P 500 lost 4.29 points, or 0.17 percent, to 2,581.35 and the Nasdaq Composite dropped 4.05 points, or 0.06 percent, to 6,789.25.

The benchmark S&P 500 has rallied more than 15 percent this year, supported by corporate earnings growth and solid economic data.

With nearly all of the S&P 500 companies reporting results, third-quarter earnings are expected to have climbed 8.2 percent, according to Thomson Reuters I/B/E/S.

Twenty-First Century Fox shares rose 4.8 percent after two people familiar with the situation said both Comcast and Verizon were interested in buying parts of its studio and TV operations.

Advancing issues outnumbered declining ones on the NYSE by a 1.81-to-1 ratio; on Nasdaq, a 1.56-to-1 ratio favored advancers. (Additional reporting by Sruthi Shankar in Bengaluru; Editing by Anil D'Silva and James Dalgleish)